[255] | 1 | // -*- C++ -*- |
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| 2 | |
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[373] | 3 | #ifndef HUGO_FIB_HEAP_H |
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| 4 | #define HUGO_FIB_HEAP_H |
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[255] | 5 | |
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| 6 | ///\file |
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| 7 | ///\brief Fibonacci Heap implementation. |
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| 8 | |
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| 9 | #include <vector> |
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| 10 | #include <functional> |
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| 11 | #include <math.h> |
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| 12 | |
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| 13 | namespace hugo { |
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| 14 | |
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[373] | 15 | /// An implementation of the Fibonacci Heap. |
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| 16 | |
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| 17 | /** |
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| 18 | This class implements the \e Fibonacci \e heap data structure. A \e |
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| 19 | heap is a data structure for storing items with specified priorities, |
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| 20 | such that finding the item with minimum priority is efficient. In a |
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| 21 | heap one can change the priority of an item, and to add or erase an |
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| 22 | item. |
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| 23 | |
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| 24 | The methods \ref increase and \ref erase are not efficient, in |
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| 25 | case of many calls to these operations, it is better to use |
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| 26 | a binary heap. |
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| 27 | |
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| 28 | /param Item The type of the items to be stored. |
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| 29 | /param Prio The type of the priority of the items. |
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| 30 | /param ItemIntMap A read and writable Item int map, for the usage of |
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| 31 | the heap. |
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| 32 | /param Compare A class for the comparison of the priorities. The |
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| 33 | default is \c std::less<Prio>. |
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| 34 | |
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| 35 | */ |
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| 36 | |
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| 37 | #ifdef DOXYGEN |
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| 38 | template <typename Item, |
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| 39 | typename Prio, |
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| 40 | typename ItemIntMap, |
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| 41 | typename Compare> |
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| 42 | #else |
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| 43 | template <typename Item, |
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| 44 | typename Prio, |
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| 45 | typename ItemIntMap, |
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[255] | 46 | typename Compare = std::less<Prio> > |
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[373] | 47 | #endif |
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[255] | 48 | class FibHeap { |
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[373] | 49 | public: |
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[255] | 50 | typedef Prio PrioType; |
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| 51 | |
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[373] | 52 | private: |
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[255] | 53 | class store; |
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| 54 | |
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| 55 | std::vector<store> container; |
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| 56 | int minimum; |
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| 57 | ItemIntMap &iimap; |
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| 58 | Compare comp; |
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| 59 | int num_items; |
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[373] | 60 | |
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[255] | 61 | ///\todo It is use nowhere |
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| 62 | ///\todo It doesn't conform to the naming conventions. |
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| 63 | public: |
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| 64 | enum state_enum { |
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| 65 | IN_HEAP = 0, |
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| 66 | PRE_HEAP = -1, |
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| 67 | POST_HEAP = -2 |
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| 68 | }; |
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| 69 | |
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| 70 | public : |
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| 71 | |
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[373] | 72 | FibHeap(ItemIntMap &_iimap) : minimum(0), iimap(_iimap), num_items() {} |
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| 73 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), |
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[255] | 74 | iimap(_iimap), comp(_comp), num_items() {} |
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| 75 | |
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[373] | 76 | ///The number of items stored in the heap. |
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| 77 | |
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| 78 | /** |
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| 79 | Returns the number of items stored in the heap. |
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| 80 | */ |
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| 81 | int size() const { return num_items; } |
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| 82 | |
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| 83 | ///Checks if the heap stores no items. |
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[255] | 84 | |
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[373] | 85 | /** |
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| 86 | Returns true iff the heap stores no items. |
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| 87 | */ |
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| 88 | bool empty() const { return num_items==0; } |
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| 89 | |
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| 90 | ///Item \c item gets to the heap with priority \c value independently if \c item was already there. |
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| 91 | |
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| 92 | /** |
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| 93 | This method calls \ref push(item, value) if \c item is not |
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| 94 | stored in the heap, and it calls \ref decrease(it, \c value) or |
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| 95 | \ref increase(it, \c value) otherwise. |
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| 96 | */ |
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| 97 | void set (Item const item, PrioType const value); //vigyazat: az implementacioban it van |
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| 98 | |
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| 99 | ///Adds \c item to the heap with priority \c value. |
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| 100 | |
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| 101 | /** |
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| 102 | Adds \c item to the heap with priority \c value. |
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| 103 | \pre \c item must not be stored in the heap. |
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| 104 | */ |
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| 105 | void push (Item const it, PrioType const value); /*vigyazat: az implementacioban it van*/ |
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| 106 | |
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| 107 | |
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| 108 | ///Returns the item having the minimum priority w.r.t. Compare. |
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| 109 | |
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| 110 | /** |
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| 111 | This method returns the item having the minimum priority w.r.t. Compare. |
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| 112 | \pre The heap must be nonempty. |
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| 113 | */ |
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| 114 | Item top() const { return container[minimum].name; } |
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| 115 | |
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| 116 | |
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| 117 | ///Returns the minimum priority w.r.t. Compare. |
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| 118 | |
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| 119 | /** |
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| 120 | It returns the minimum priority w.r.t. Compare. |
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| 121 | \pre The heap must be nonempty. |
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| 122 | */ |
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| 123 | PrioType prio() const { return container[minimum].prio; } |
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| 124 | |
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| 125 | |
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| 126 | ///Returns the priority of \c item. |
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| 127 | |
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| 128 | /** |
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| 129 | It returns the priority of \c item. |
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| 130 | \pre \c item must be in the heap. |
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| 131 | */ |
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| 132 | PrioType& operator[](const Item& it) { return container[iimap[it]].prio; } |
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| 133 | |
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| 134 | ///Returns the priority of \c item. |
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| 135 | |
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| 136 | /** |
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| 137 | It returns the priority of \c item. |
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| 138 | \pre \c item must be in the heap. |
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| 139 | */ |
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| 140 | const PrioType& operator[](const Item& it) const { |
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| 141 | return container[iimap[it]].prio; |
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[255] | 142 | } |
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| 143 | |
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| 144 | |
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[373] | 145 | ///Deletes the item with minimum priority w.r.t. Compare. |
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[255] | 146 | |
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[373] | 147 | /** |
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| 148 | This method deletes the item with minimum priority w.r.t. |
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| 149 | Compare from the heap. |
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| 150 | \pre The heap must be non-empty. |
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| 151 | */ |
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| 152 | void pop(); |
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| 153 | |
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| 154 | ///Deletes \c item from the heap. |
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| 155 | |
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| 156 | /** |
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| 157 | This method deletes \c item from the heap, if \c item was already |
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| 158 | stored in the heap. It is quite inefficient in Fibonacci heaps. |
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| 159 | */ |
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| 160 | void erase (const Item& item); /*vigyazat: az implementacioban it van*/ |
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| 161 | |
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| 162 | ///Decreases the priority of \c item to \c value. |
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| 163 | |
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| 164 | /** |
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| 165 | This method decreases the priority of \c item to \c value. |
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| 166 | \pre \c item must be stored in the heap with priority at least \c |
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| 167 | value w.r.t. Compare. |
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| 168 | */ |
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| 169 | void decrease (Item item, PrioType const value); /*vigyazat: az implementacioban it van*/ |
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| 170 | |
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| 171 | |
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| 172 | ///Increases the priority of \c item to \c value. |
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| 173 | |
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| 174 | /** |
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| 175 | This method sets the priority of \c item to \c value. Though |
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| 176 | there is no precondition on the priority of \c item, this |
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| 177 | method should be used only if one wants to \e increase |
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| 178 | (w.r.t. Compare) the priority of \c item, because this |
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| 179 | method is inefficient. |
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| 180 | */ |
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| 181 | void increase (Item it, PrioType const value) { |
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| 182 | erase(it); |
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| 183 | push(it, value); |
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| 184 | } |
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| 185 | |
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| 186 | |
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| 187 | ///Tells if \c item is in, was in, or has not been in the heap. |
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| 188 | |
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| 189 | /** |
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| 190 | This method returns PRE_HEAP if \c item has never been in the |
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| 191 | heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 192 | otherwise. In the latter case it is possible that \c item will |
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| 193 | get back to the heap again. |
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| 194 | */ |
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| 195 | state_enum state(const Item &it); /*vigyazat: az implementacioban it van*/ |
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| 196 | |
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| 197 | |
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| 198 | |
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| 199 | // ********************************************************************** |
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| 200 | // IMPLEMENTATIONS |
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| 201 | // ********************************************************************** |
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| 202 | |
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[255] | 203 | |
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| 204 | void set (Item const it, PrioType const value) { |
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| 205 | int i=iimap[it]; |
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| 206 | if ( i >= 0 && container[i].in ) { |
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| 207 | if ( comp(value, container[i].prio) ) decrease(it, value); |
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| 208 | if ( comp(container[i].prio, value) ) increase(it, value); |
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| 209 | } else push(it, value); |
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| 210 | } |
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| 211 | |
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| 212 | |
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| 213 | void push (Item const it, PrioType const value) { |
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| 214 | int i=iimap[it]; |
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| 215 | if ( i < 0 ) { |
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| 216 | int s=container.size(); |
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| 217 | iimap.set( it, s ); |
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| 218 | store st; |
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| 219 | st.name=it; |
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| 220 | container.push_back(st); |
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| 221 | i=s; |
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| 222 | } else { |
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| 223 | container[i].parent=container[i].child=-1; |
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| 224 | container[i].degree=0; |
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| 225 | container[i].in=true; |
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| 226 | container[i].marked=false; |
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| 227 | } |
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| 228 | |
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| 229 | if ( num_items ) { |
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| 230 | container[container[minimum].right_neighbor].left_neighbor=i; |
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| 231 | container[i].right_neighbor=container[minimum].right_neighbor; |
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| 232 | container[minimum].right_neighbor=i; |
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| 233 | container[i].left_neighbor=minimum; |
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| 234 | if ( comp( value, container[minimum].prio) ) minimum=i; |
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| 235 | } else { |
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| 236 | container[i].right_neighbor=container[i].left_neighbor=i; |
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| 237 | minimum=i; |
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| 238 | } |
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| 239 | container[i].prio=value; |
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| 240 | ++num_items; |
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| 241 | } |
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| 242 | |
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| 243 | |
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| 244 | void pop() { |
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| 245 | /*The first case is that there are only one root.*/ |
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| 246 | if ( container[minimum].left_neighbor==minimum ) { |
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| 247 | container[minimum].in=false; |
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| 248 | if ( container[minimum].degree!=0 ) { |
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| 249 | makeroot(container[minimum].child); |
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| 250 | minimum=container[minimum].child; |
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| 251 | balance(); |
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| 252 | } |
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| 253 | } else { |
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| 254 | int right=container[minimum].right_neighbor; |
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| 255 | unlace(minimum); |
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| 256 | container[minimum].in=false; |
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| 257 | if ( container[minimum].degree > 0 ) { |
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| 258 | int left=container[minimum].left_neighbor; |
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| 259 | int child=container[minimum].child; |
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| 260 | int last_child=container[child].left_neighbor; |
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| 261 | |
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| 262 | makeroot(child); |
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| 263 | |
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| 264 | container[left].right_neighbor=child; |
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| 265 | container[child].left_neighbor=left; |
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| 266 | container[right].left_neighbor=last_child; |
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| 267 | container[last_child].right_neighbor=right; |
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| 268 | } |
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| 269 | minimum=right; |
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| 270 | balance(); |
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| 271 | } // the case where there are more roots |
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| 272 | --num_items; |
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| 273 | } |
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| 274 | |
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| 275 | |
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| 276 | void erase (const Item& it) { |
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| 277 | int i=iimap[it]; |
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| 278 | |
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| 279 | if ( i >= 0 && container[i].in ) { |
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| 280 | if ( container[i].parent!=-1 ) { |
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| 281 | int p=container[i].parent; |
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| 282 | cut(i,p); |
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| 283 | cascade(p); |
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| 284 | } |
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| 285 | minimum=i; //As if its prio would be -infinity |
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| 286 | pop(); |
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| 287 | } |
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| 288 | } |
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| 289 | |
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| 290 | |
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| 291 | void decrease (Item it, PrioType const value) { |
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| 292 | int i=iimap[it]; |
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| 293 | container[i].prio=value; |
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| 294 | int p=container[i].parent; |
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| 295 | |
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| 296 | if ( p!=-1 && comp(value, container[p].prio) ) { |
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| 297 | cut(i,p); |
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| 298 | cascade(p); |
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| 299 | } |
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| 300 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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| 301 | } |
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| 302 | |
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| 303 | |
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| 304 | state_enum state(const Item &it) const { |
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| 305 | int i=iimap[it]; |
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| 306 | if( i>=0 ) { |
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| 307 | if ( container[i].in ) i=0; |
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| 308 | else i=-2; |
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| 309 | } |
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| 310 | return state_enum(i); |
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| 311 | } |
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| 312 | |
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| 313 | |
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| 314 | private: |
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| 315 | |
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| 316 | void balance() { |
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| 317 | |
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| 318 | int maxdeg=int( floor( 2.08*log(double(container.size()))))+1; |
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| 319 | |
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| 320 | std::vector<int> A(maxdeg,-1); |
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| 321 | |
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| 322 | /* |
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| 323 | *Recall that now minimum does not point to the minimum prio element. |
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| 324 | *We set minimum to this during balance(). |
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| 325 | */ |
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| 326 | int anchor=container[minimum].left_neighbor; |
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| 327 | int next=minimum; |
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| 328 | bool end=false; |
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| 329 | |
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| 330 | do { |
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| 331 | int active=next; |
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| 332 | if ( anchor==active ) end=true; |
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| 333 | int d=container[active].degree; |
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| 334 | next=container[active].right_neighbor; |
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| 335 | |
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| 336 | while (A[d]!=-1) { |
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| 337 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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| 338 | fuse(active,A[d]); |
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| 339 | } else { |
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| 340 | fuse(A[d],active); |
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| 341 | active=A[d]; |
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| 342 | } |
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| 343 | A[d]=-1; |
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| 344 | ++d; |
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| 345 | } |
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| 346 | A[d]=active; |
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| 347 | } while ( !end ); |
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| 348 | |
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| 349 | |
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| 350 | while ( container[minimum].parent >=0 ) minimum=container[minimum].parent; |
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| 351 | int s=minimum; |
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| 352 | int m=minimum; |
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| 353 | do { |
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| 354 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
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| 355 | s=container[s].right_neighbor; |
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| 356 | } while ( s != m ); |
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| 357 | } |
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| 358 | |
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| 359 | |
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| 360 | void makeroot (int c) { |
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| 361 | int s=c; |
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| 362 | do { |
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| 363 | container[s].parent=-1; |
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| 364 | s=container[s].right_neighbor; |
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| 365 | } while ( s != c ); |
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| 366 | } |
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| 367 | |
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| 368 | |
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| 369 | void cut (int a, int b) { |
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| 370 | /* |
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| 371 | *Replacing a from the children of b. |
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| 372 | */ |
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| 373 | --container[b].degree; |
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| 374 | |
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| 375 | if ( container[b].degree !=0 ) { |
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| 376 | int child=container[b].child; |
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| 377 | if ( child==a ) |
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| 378 | container[b].child=container[child].right_neighbor; |
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| 379 | unlace(a); |
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| 380 | } |
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| 381 | |
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| 382 | |
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| 383 | /*Lacing a to the roots.*/ |
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| 384 | int right=container[minimum].right_neighbor; |
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| 385 | container[minimum].right_neighbor=a; |
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| 386 | container[a].left_neighbor=minimum; |
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| 387 | container[a].right_neighbor=right; |
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| 388 | container[right].left_neighbor=a; |
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| 389 | |
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| 390 | container[a].parent=-1; |
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| 391 | container[a].marked=false; |
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| 392 | } |
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| 393 | |
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| 394 | |
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| 395 | void cascade (int a) |
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| 396 | { |
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| 397 | if ( container[a].parent!=-1 ) { |
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| 398 | int p=container[a].parent; |
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| 399 | |
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| 400 | if ( container[a].marked==false ) container[a].marked=true; |
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| 401 | else { |
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| 402 | cut(a,p); |
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| 403 | cascade(p); |
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| 404 | } |
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| 405 | } |
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| 406 | } |
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| 407 | |
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| 408 | |
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| 409 | void fuse (int a, int b) { |
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| 410 | unlace(b); |
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| 411 | |
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| 412 | /*Lacing b under a.*/ |
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| 413 | container[b].parent=a; |
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| 414 | |
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| 415 | if (container[a].degree==0) { |
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| 416 | container[b].left_neighbor=b; |
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| 417 | container[b].right_neighbor=b; |
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| 418 | container[a].child=b; |
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| 419 | } else { |
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| 420 | int child=container[a].child; |
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| 421 | int last_child=container[child].left_neighbor; |
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| 422 | container[child].left_neighbor=b; |
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| 423 | container[b].right_neighbor=child; |
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| 424 | container[last_child].right_neighbor=b; |
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| 425 | container[b].left_neighbor=last_child; |
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| 426 | } |
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| 427 | |
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| 428 | ++container[a].degree; |
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| 429 | |
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| 430 | container[b].marked=false; |
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| 431 | } |
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| 432 | |
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| 433 | |
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| 434 | /* |
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| 435 | *It is invoked only if a has siblings. |
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| 436 | */ |
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| 437 | void unlace (int a) { |
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| 438 | int leftn=container[a].left_neighbor; |
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| 439 | int rightn=container[a].right_neighbor; |
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| 440 | container[leftn].right_neighbor=rightn; |
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| 441 | container[rightn].left_neighbor=leftn; |
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| 442 | } |
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| 443 | |
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| 444 | |
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| 445 | class store { |
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| 446 | friend class FibHeap; |
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| 447 | |
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| 448 | Item name; |
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| 449 | int parent; |
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| 450 | int left_neighbor; |
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| 451 | int right_neighbor; |
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| 452 | int child; |
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| 453 | int degree; |
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| 454 | bool marked; |
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| 455 | bool in; |
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| 456 | PrioType prio; |
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| 457 | |
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| 458 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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| 459 | }; |
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| 460 | |
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| 461 | }; |
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| 462 | |
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| 463 | } //namespace hugo |
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| 464 | #endif |
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